On matroid modularity and the coefficients of the inverse Kazhdan-Lusztig polynomial of a matroid
arXiv:2103.08580
Abstract
Following the work of Gao and Xie in [2], we state some properties of the inverse Kazhdan-Lusztig polynomial of a matroid. We also give partial answers to a conjecture that states that regular connected matroids are non-degenerate. We link the degeneracy of a matroid to the inverse Kazhdan-Lusztig polynomial and we show that the Conjecture holds for modular matroids, by proving that degenerate modular matroids are not regular.
arXiv comment9 pages v2 updated after mistake was found in a proof v3 section of new results expanded and divided into two new sections; added new results of non-degeneracy on even-rank matroids